In mathematics, the large Veblen ordinal is a certain large countable ordinal

Large countable ordinal

In the mathematical discipline of set theory, there are many ways of describing specific countable ordinals. The smallest ones can be usefully and non-circularly expressed in terms of their Cantor normal forms. Beyond that, many ordinals of relevance to proof theory still have computable ordinal...

, named after Oswald Veblen

Oswald Veblen

Oswald Veblen was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905.-Life:...

.

There is no standard notation for ordinals beyond the Feferman–Schütte ordinal

Feferman–Schütte ordinal

In mathematics, the Feferman–Schütte ordinal Γ0 is a large countable ordinal.It is the proof theoretic ordinal of several mathematical theories, such as arithmetical transfinite recursion.It is named after Solomon Feferman and Kurt Schütte....

 Γ₀. Most systems of notation use symbols such as ψ(α), θ(α), ψ_α(β), some of which are modifications of the Veblen function

Veblen function

In mathematics, the Veblen functions are a hierarchy of normal functions , introduced by Oswald Veblen in...

s to produce countable ordinals even for uncountable arguments, and some of which are "collapsing functions".

The large Veblen ordinal is sometimes denoted by or or . It was constructed by Veblen using an extension of Veblen functions allowing infinitely many arguments.